I raised a cottontail once but it was older than yours.
Cottontail rabbits are difficult to successfully raise.
Below is my recollection, but we found the information from a Google search.
You need to get the dog milk powder and mix it with heavy cream. The milk/cream will be extremely thick and you will need to make the opening of the nipple larger. You need to squeeze the cream into its mouth but make sure you do not over feed it. Early on you might also need to massage its anus to get it to poop.
The first few days the rabbit will need to be fed every two hours then every four hours until it eventually gets large enough to eat twice a day. Expect a couple sleepless nights.
Before it can begin eating grasses etc. it needs special enzymes that it gets from eating its mother's poop. We got some rabbit poop from a breeder and mixed it with a batch of the milk. The instructions said that Tractor Supply might have a supplement that includes the enzyme, but we couldn't find it anywhere. Without this enzyme, it cannot digest grass and cannot survive.
Once it gets large enough to eat rabbit food, you can feed it rabbit pellets and alfalfa from the pet store, but it will also need a lot clover and various grasses from your yard/field. Wild rabbits need a wider variety diet than domestic rabbits. It will grow fast. Mine would sit in my lap as we watched TV.
Note, after taking care of the rabbit for several weeks, I tried to take it to two rehab organizations because I was going on a business trip. Nether would take it because I had raised it. They did ask if I would volunteer to help with raising rabbits. Apparently, successfully raising cottontail rabbits is difficult and they like to recruit those who have done it.
Note also that unless things have changed, being in possession of and transporting a cottontail rabbit is not restricted in Texas. By the time I let that little guy go, it had traveled a hundreds of miles through the Brazos Valley and the Houston metropolitan region.